Polynomial ballisticity conditions and invariance principle for random walks in strong mixing environments

• 成果类型: Article
• 署名作者: Guerra, Enrique; Valle, Glauco; Vares, Maria Eulalia
• 署名单位: Hebrew University of Jerusalem; Universidade Federal do Rio de Janeiro
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-021-01106-9
• 发表日期: 2022
• 页码: 685-750
• 关键词: CENTRAL-LIMIT-THEOREM; large numbers; LAW; BEHAVIOR

摘要

We study ballisticity conditions for d-dimensional random walks in strong mixing environments, with underlying dimension d >= 2. Specifically, we introduce an effective polynomial condition similar to that given by Berger et al. (Comm. Pure Appl. Math. 77:1947-1973, 2014). In a mixing setup we prove that this condition implies the corresponding stretched exponential decay, and obtain an annealed functional central limit theorem for the random walk process centered at the limiting velocity. This paper complements previous work of Guerra (Ann. Probab. 47:3003-3054, 2019) and completes the answer about the meaning of condition (T')vertical bar l in a mixing setting, an open question posed by Comets and Zeitouni (Ann. Probab. 32:880-914, 2004).